Sorry, you're right about Emigrant. There is a faucet there along side the privy [not connected I assume! );-0 ], but I've never used it. I try to stay away from what the NPS calls "potable water" as it can be really brackish; good, relatively speaking, if you are out of it, but not something that may not cause you lower GI distress. The faucet at the Grapevine kiosk comes to mind. I've not gone up to the Wildrose campsite but it is categorized as a regular campsite, which should have water. YMMV on that one. When you say Panamint, I assume you are referring to Panamint Springs, on CA190. It's about 3½ miles up the fan on CA190 from the Panamint Valley Rd. intersection, your loop return from Wildrose Canyon Rd. It's a resort, and has a gas station, general store, snack bar/restaurant, campsites, and a small motel. No info on Aguereberry Point either; the road out there is classified as "graded gravel".
My buddy has been after me for the past 7-8 years to head over to Wildrose and then hike up Telescope Peak! AND, in spite of his persistence, I've managed to avoid it!
The 2-way lower end of the Titus Canyon entrance is the "freeway" portion. Once deep into the canyon, and then on towards the Leadville ruins it gets pretty irregular. As it's a one way road downward to the lower trail head, I don't know what the NPS would say about a cyclist going UP thru the canyon; it would be a fairly stiff climb to the 1st [eastbound] ridge summit [Red Pass, IIRC]. East from there is a valley - about a 2000' drop, and then another climb up to the 2nd ridge line at approximately the same altitude. If you're planning on camping along the way make sure you have plenty of supplies as there aren't even scavengers out there! The turn to Rhyolite is about 2 miles east of the Titus Canyon entry point, and Beatty is another 4 miles beyond Rhyolite.
I would guess that of the loop routes you're considering, the Titus Canyon would be the tougher and more time consuming. It has 25 miles of so-called gravel road and some really significant elevation changes. From FC you have to summit Daylight Pass [4317'] and then drop down to the NV high desert which averages 2800-3000'; that's where Titus Canyon Rd starts from. BTW, Beatty is at 3280'; it's on a small ridge. Titus has the 2 ridge lines, each in the 5500' range; Red Pass and "a player to be named later". All of this starts at FC, -178'!
As for weather in March, you can expect just about ANYTHING and you'll be safe! In the high elevation areas in can be damned cold - mid/low 30's - overnight, with highs peaking in the the mid/low 60's daytime. There won't be any snow to be concerned about as we've not had much precipitation and the snow levels haven't been below 8-9000' when we've had it. SUBJECT TO CHANGE WITHOUT NOTICE, of course....
BTW, AAA has a pretty good map of Death Valley if you're a member; it's just DV by itself. Also, when you check in at the VC you will get a visitor's map along with your park pass. Ask them for a copy of the "Backcountry Roads" edition; they don't normally hand them out.
YMMV
-dg